The Proposed Constitutional Amendments to the Local Finance Article: A Critical Analysis

This paper examines the recent proposals of the Committee on Municipal Affairs of the Association of the Bar of the City of New York to amend Article VIII of the New York State Constitution. These amendments would modify the powers of local governments to raise and spend money. The paper considers philosophical, political and judicial theories of local finance, and summarizes the effects of the proposals, concluding that they have merit and should be explored

Strong Stability Preserving Two-Step Runge-Kutta Methods

We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple\ud subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order WENO discretizations

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Bone Marrow–Derived Antigen-Presenting Cells Are Required for the Generation of Cytotoxic T Lymphocyte Responses to Viruses and Use Transporter Associated with Antigen Presentation (Tap)-Dependent and -Independent Pathways of Antigen Presentation

Bone marrow (BM)-derived professional antigen-presenting cells (pAPCs) are required for the generation of cytotoxic T lymphocyte (CTL) responses to vaccinia virus and poliovirus. Furthermore, these BM-derived pAPCs require a functional transporter associated with antigen presentation (TAP). In this report we analyze the requirements for BM-derived pAPCs and TAP in the initiation of CTL responses to lymphocytic choriomeningitis virus (LCMV) and influenza virus (Flu). Our results indicate a requirement for BM-derived pAPCs for the CTL responses to these viruses. However, we found that the generation of CTLs to one LCMV epitope (LCMV nucleoprotein 396–404) was dependent on BM-derived pAPCs but, surprisingly, TAP independent. The study of the CTL response to Flu confirmed the existence of this BM-derived pAPC-dependent/TAP-independent CTL response and indicated that the TAP-independent pathway is ∼10–300-fold less efficient than the TAP-dependent pathway